Preheat oven to 375 degrees F (190 degrees C) and grease a 9x13 inch baking dish.
Cook penne pasta in boiling salted water until al dente, then drain.
In a large skillet over medium heat, melt the butter and sauté minced garlic for 1 minute until fragrant.
Whisk in heavy cream and simmer for 5 minutes.
Stir in parmesan cheese, salt, and pepper until cheese is melted and sauce thickens.
Combine pasta, chicken, and sauce in a large bowl and toss until evenly coated.
Transfer mixture to the baking dish and top with shredded mozzarella cheese.
Bake for 20 minutes until the cheese is melted and bubbling.
Garnish with fresh parsley before serving.